McqMate
Chapters
1. 
Let A={a, b, {c, d}, e}. How many elements does A contain? 
A.  1 
B.  2 
C.  3 
D.  4 
Answer» D. 4 
2. 
Let A={2,{4,5},4} Which statement is correct? 
A.  5 is an element of A. 
B.  {5} is an element of A. 
C.  {4, 5} is an element of A. 
D.  {5} is a subset of A. 
Answer» C. {4, 5} is an element of A. 
3. 
Which of these sets is finite? 
A.  {x  x is even} 
B.  ) {1, 2, 3,...} 
C.  {1, 2, 3,...,999,1000} 
D.  none 
Answer» C. {1, 2, 3,...,999,1000} 
4. 
Which of these sets is not a null set? 
A.  A = {x  6x = 24 and 3x = 1} 
B.  B = {x  x + 10 = 10} 
C.  C = {x  x is a man older than 200 years} 
D.  D = {x  x < x} 
Answer» B. B = {x  x + 10 = 10} 
5. 
. Let S={1, 2, 3}. How many subsets does S contain? 
A.  3 
B.  6 
C.  8 
D.  4 
Answer» C. 8 
6. 
. Which set S does the power set 2S = {Ф,{1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}} come from? 
A.  {{1},{2},{3}} 
B.  {1, 2, 3} 
C.  {{1, 2}, {2, 3}, {1, 3}} 
D.  {{1, 2, 3}} 
Answer» B. {1, 2, 3} 
7. 
Let A = {x, y, z}, B = {v, w, x}. Which of the following statements is correct? 
A.  A U B ={v, w, x, y, z} 
B.  A U B = {v, w, y, z} 
C.  A U B = {v, w, x, y} 
D.  A U B ={x, w, x, y, z} 
Answer» A. A U B ={v, w, x, y, z} 
8. 
which sets are equal ? 1.{r,s,t} 2.{s,s,t,r} 3.{t,r,t,s} 
A.  1 and 2 
B.  2 and 3 
C.  1 and 3 
D.  all are equal 
Answer» D. all are equal 
9. 
A U A=A according to …….law 
A.  Associative law 
B.  commutative law 
C.  Indempotent law 
D.  distributive law 
Answer» C. Indempotent law 
10. 
In any application of the theory of sets, the members of all the sets belongs to …… set 
A.  union 
B.  intersection 
C.  universal 
D.  cardinal 
Answer» C. universal 
11. 
let A={{a,b}} then aЄ A 
A.  TRUE 
B.  FALSE 
C.  Both 
D.  None 
Answer» B. FALSE 
12. 
ФЄФ 
A.  TRUE 
B.  FALSE 
C.  Both 
D.  None 
Answer» B. FALSE 
13. 
The sets {a,b,c} and {b,c,a} represnet the same sets. 
A.  TRUE 
B.  FALSE 
C.  Both 
D.  None 
Answer» A. TRUE 
14. 
Cardinality of a set is number of element of the set. 
A.  TRUE 
B.  FALSE 
C.  Both 
D.  None 
Answer» A. TRUE 
15. 
Multiset is an unordered collection of elemnts where an element can occur a a member more than once 
A.  TRUE 
B.  FALSE 
C.  Both 
D.  None 
Answer» A. TRUE 
16. 
one of the A or B is uncountably infinite and one is countably infinite then  AUB will be 
A.  countably infinite 
B.  uncountably finite 
C.  countably finite 
D.  uncountably infinite 
Answer» D. uncountably infinite 
17. 
Sum of first n positive integers is 
A.  n(n+1) 
B.  n 
C.  n(n+1)0.5 
D.  n(n+2) 
Answer» C. n(n+1)0.5 
18. 
Let P(S) denote the power set of set S. which of the is always true 
A.  P(P(s))=p(s) 
B.  P(S)∩ S= P(S) 
C.  P(S)∩P(P(S)) ={Ф} 
D.  None 
Answer» C. P(S)∩P(P(S)) ={Ф} 
19. 
{3}Є{1,3,5} 
A.  TRUE 
B.  FALSE 
C.  Both 
D.  None 
Answer» B. FALSE 
20. 
consider the following data for 120 mathematics students at a college concerning the languages French,Gernan, and russian: 65 study frensh, 45 study german 42 study russian , 20 study french and german, 25 study french and russian, 15 study german and russian. 8 study all three languages. Determine how many students study exactly 1 subject? 
A.  100 
B.  25 
C.  56 
D.  20 
Answer» C. 56 
21. 
……… is an unordered collection of elements where an element can occur as a member more than once 
A.  Multiset 
B.  ordered set 
C.  set 
D.  None 
Answer» A. Multiset 
22. 
In a room containing 28 females, there are 18 females who speak English, 15 females speak french and 22 speak german. 9 females speak both english and french, 11 females speak both french and german where as 13 speak both german and english. How many females speak all 3 languages? 
A.  9 
B.  8 
C.  7 
D.  6 
Answer» D. 6 
23. 
If U = {1, 2, 3, . . . 10 } and S = { 4, 5, 6, 7, 8 }, then S ' = 
A.  { 9, 10 } 
B.  {1, 2, 3 } 
C.  {1, 2, 3 9 } 
D.  {1, 2, 3 9 10 } 
Answer» D. {1, 2, 3 9 10 } 
24. 
If U = {1, 2, 3, . . . 20 } and S = set of prime numbers , then S = 
A.  { 3, 5, 7, 11, 13, 17 } 
B.  { 2, 3, 5, 7, 11, 13, 17, 19 } 
C.  {1, 3, 5, 7, 9, 11, 13, 15, 17, 19 } 
D.  {1, 2, 3, 5, 7, 11, 13, 17 } 
Answer» B. { 2, 3, 5, 7, 11, 13, 17, 19 } 
25. 
Consider the statement,“If n is divisible by 30 then n is divisible by 2 and by 3 and by 5.”Which of the following statements is equivalent to this statement? 
A.  If n is not divisible by 30 then n is divisible by 2 or divisible by 3 or divisible by 5 
B.  If n is not divisible by 30 then n is not divisible by 2 or not divisible by 3 or not divisible by 5 
C.  If n is divisible by 2 and divisible by 3 and divisible by 5 then n is divisible by 30. 
D.  If n is not divisible by 2 or not divisible by 3 or not divisible by 5 then n is not divisible by 30 
Answer» D. If n is not divisible by 2 or not divisible by 3 or not divisible by 5 then n is not divisible by 30 
26. 
Which of the following statements is the contrapositive of the statement, “You win the game if you know the rules but are not overconfident.” 
A.  If you lose the game then you don’t know the rules or you are overconfident. 
B.  A sufficient condition that you win the game is that you know the rules or you are not over confident 
C.  If you don’t know the rules or are overconfident you lose the game. 
D.  If you know the rules and are overconfiden t then you win the game. 
Answer» A. If you lose the game then you don’t know the rules or you are overconfident. 
27. 
A sufficient condition that a triangle T be a right triangle is that a2 + b2 = c2. An equivalent statement is 
A.  If T is a right triangle then a2 + b2 = c2. 
B.  If a2 + b2 = c2 then T is a right triangle. 
C.  If a2 + b2 6= c2 then T is not a right triangle. 
D.  T is a right triangle only if a2 + b2 = c2. 
Answer» B. If a2 + b2 = c2 then T is a right triangle. 
28. 
Which of the following is the inverse of the statement: " If I eat a mango than I do not drink milk". 
A.  I drink milk only if I do not eat a mango 
B.  If I don’t eat a mango then I drink milk 
C.  If I do not drink milk then I eat mango 
D.  None 
Answer» B. If I don’t eat a mango then I drink milk 
29. 
If p= It is hot, and q= It is sultry, which of the following sentences in the appropriate version for the symbolic expression: p٨ q 
A.  If it is sultry then it is hot 
B.  It is sultry only if it is hot 
C.  It is sultry and it is not hot 
D.  None 
Answer» D. None 
30. 
which of the following is the contrapositive of the statement: " A quadrilateral is a square only if it is both rectangle and a rhombus". 
A.  If a rectangle is not a a rhombus it is not a square 
B.  If a rhombus is not rectangle it is not a square 
C.  If a quadrilateral is neither a rectangle nor a rhombus then it is not a square 
D.  None 
Answer» C. If a quadrilateral is neither a rectangle nor a rhombus then it is not a square 
31. 
For a conditional statement p===>q, which of the following is incorrect. 
A.  Converse of the inverse is its contrapositive 
B.  contrapositive of the converse is its inverse 
C.  Inverse of the contrapositiv e is its converse 
D.  None 
Answer» D. None 
32. 
Which of the following is equivalent to p==>q 
A.  ~xp٨q 
B.  pV~q 
C.  ~xpVq 
D.  pV~q 
Answer» C. ~xpVq 
33. 
Equivalent inverse of p==>q is 
A.  ~xp٨q 
B.  pV~q 
C.  ~xpVq 
D.  pV~q 
Answer» D. pV~q 
34. 
Converse of p==>q is 
A.  ~xp٨q 
B.  pV~q 
C.  ~xpVq 
D.  pV~q 
Answer» D. pV~q 
35. 
the truth table for exclusive disjunction will be 
A.  tautology 
B.  Contradiction 
C.  Logical equivalent 
D.  p or q but not both 
Answer» D. p or q but not both 
36. 
The conditional statement p→q and its contrapositive are…. 
A.  Converse 
B.  Inverse 
C.  Logically equivalent 
D.  None 
Answer» C. Logically equivalent 
37. 
Set A has 3 elements, set B has 6 elements, then the minimum number of elements in A U B is …. 
A.  3 
B.  6 
C.  9 
D.  None 
Answer» B. 6 
38. 
Set A has 3 elements, set B has 6 elements, then the minimum number of elements in A U B is …. 
A.  6 
B.  9 
C.  18 
D.  None 
Answer» B. 9 
39. 
if P∩ Q= Ф then P U Q' is 
A.  P 
B.  UP 
C.  UQ 
D.  Ф 
Answer» C. UQ 
40. 
The number of proper subset of {1,2,3,4} is 
A.  16 
B.  15 
C.  10 
D.  12 
Answer» A. 16 
41. 
Consider the four statements: 1.(q==>p)٨(~p) 2. p==>(~q) V r 3. ~p==>~(p٨q) 4.p٨q٨~(pVq) Which one is tautology. 
A.  A 
B.  B 
C.  C 
D.  D 
Answer» C. C 
42. 
Which among the statements given in Q.70 is contradiction 
A.  A 
B.  B 
C.  C 
D.  D 
Answer» D. D 
43. 
Consider the four statements 1.p٨~q↔~p V q 2.p٨(~p Vq)٨(~q) 3.(pV(~q))٨ ~((~p)Vq) 4.~(p↔q)↔(p↔~q) which one of this contradiction. 
A.  A 
B.  B 
C.  C 
D.  D 
Answer» D. D 
44. 
consider the four tsatements: 1.(p→q) ٨(p٨~q) 2.(~p→r)٨(p↔q) 3.p→(~qVr) 4.~(p٨q) V (p↔q) Which one of these four ststements is a tautology. 
A.  A 
B.  B 
C.  C 
D.  D 
Answer» D. D 
45. 
In above question which statement is contradiction. 
A.  A 
B.  B 
C.  C 
D.  D 
Answer» A. A 
46. 
Which of the following sets are equal. 1. {p,q,m,n} 2.{m,p,n,q} 3.{q,p,p,m,m,p,n} 4.{p,q,n,,n,m} 
A.  1 and 2 are equal 
B.  2 and 3 are equal 
C.  3 and 4 are equal 
D.  All are equal. 
Answer» D. All are equal. 
47. 
Consider the set A={{1,3,5},{7,9,11},{13,15}} then determine which of the following is/are true. 1.1ЄA 2.{{1,3,5}} CA 3. Ф subet of A 4. A 
A.  2 and 3 is true 
B.  1 and 3 is true 
C.  3 is true 
D.  None 
Answer» A. 2 and 3 is true 
48. 
Determine the validity of the following argument: S1: all my friends are musicians. S2: John is my friend. S3: None of my neighbours are musicians. S: John is not my neighbour. 
A.  Valid 
B.  Not valid 
C.  Both a and b 
D.  None 
Answer» A. Valid 
49. 
In a survey of 60 people , it was found that: 25 read Newsweek magzine. 26 read Time 26 read Fortune 9 read both newsweek and fortune 11 read both Newsweek and Time 8 read both Time and Fortune 3 read all 3 magzines. 1. Find the number of people who read at least one of the three magzines 
A.  30 
B.  52 
C.  40 
D.  68 
Answer» B. 52 
50. 
In above Q.78 Find the number of people who read exactly 1 magzine. 
A.  30 
B.  52 
C.  40 
D.  68 
Answer» A. 30 
51. 
In a class of 80 students , 50 students know English, 55 know french and 46 know german language. 37 students know english and french, 28 students know french and german, 7 students know none of the languages. Find out how many students know all the three languages? 
A.  73 
B.  72 
C.  50 
D.  54 
Answer» A. 73 
52. 
In above q.80 how many students exactly know 2 languages? 
A.  52 
B.  54 
C.  60 
D.  25 
Answer» B. 54 
53. 
In q. 80 how many students know exactly 1 language? 
A.  54 
B.  12 
C.  7 
D.  8 
Answer» C. 7 
54. 
A preposition is a statement that is either ture or false 
A.  TRUE 
B.  FALSE 
C.  none 
D.  both a and b 
Answer» A. TRUE 
55. 
A prepostition that is true under all circumstances is referred to as a …. 
A.  Tautology 
B.  Contradiction 
C.  Negation 
D.  Sentence 
Answer» A. Tautology 
56. 
A prepostition that is false under all circumstances is referred to as a …. 
A.  Tautology 
B.  Contradiction 
C.  Negation 
D.  Sentence 
Answer» B. Contradiction 
57. 
p→q is logically equivalent to ~p V q according to… 
A.  Identity law 
B.  Implication law 
C.  associative law 
D.  Absoption law 
Answer» B. Implication law 
58. 
A logical expression which consist of a product of elementary sum is caleed….. 
A.  Disjunctive normal form 
B.  Conjunctive normal form 
C.  Normal form 
D.  None 
Answer» B. Conjunctive normal form 
59. 
A logical expression which consist of a sum of product is caleed….. 
A.  Disjunctive normal form 
B.  Conjunctive normal form 
C.  Normal form 
D.  None 
Answer» A. Disjunctive normal form 
60. 
An assertion that contains one or more variable is called a…. 
A.  CNF 
B.  DNF 
C.  Predicates 
D.  Quantifiers 
Answer» C. Predicates 
61. 
Determine the validity of argument given: s1: If I like mathematics then I will study. S2: Either I will study or I will fail. S: If I fail then I do not mlike mathematics. 
A.  Valid 
B.  Invalid 
C.  Both a and b 
D.  none 
Answer» B. Invalid 
62. 
p V ~(p٨q) is…. 
A.  Contradiction 
B.  Tautology 
C.  predicate 
D.  None 
Answer» B. Tautology 
63. 
Determine the validity of the argument s1: If I stay up late at night , then I will be tired in the morning. S2: I stayed up last last night s: I am tired this morning. 
A.  Valid 
B.  Invalid 
C.  Both a and b 
D.  none 
Answer» A. Valid 
64. 
An argument is valid if, whenever the conclusion is true, thenthe premises are also true. 
A.  TRUE 
B.  FALSE 
C.  both a and b 
D.  none 
Answer» B. FALSE 
65. 
De Morgan's laaws are two examplesof rules of inference 
A.  TRUE 
B.  FALSE 
C.  both a and b 
D.  none 
Answer» B. FALSE 
66. 
In a club , all members participate either in tambola or the fete. 420 participate in the fete, 350 play tambola and 220 participate in both. How many members does the club have? 
A.  250 
B.  550 
C.  120 
D.  140 
Answer» B. 550 
67. 
dual of (p V q)٨ r is.. 
A.  p Vq 
B.  (p٨q) Vr 
C.  p ٨r 
D.  (p Vq) Vr 
Answer» B. (p٨q) Vr 
68. 
It was found that in first year of computer science of 80 students 50 know Cobol, 55 know C, 46 know pascal. It was also known that 37 know C and cobol, 28 know C and pascal , 25 know pascal and cobol, 7 students know none of the languages. Find how many all the 3 languages? 
A.  10 
B.  12 
C.  35 
D.  9 
Answer» B. 12 
69. 
In above q.97 How many know exactly 2 languages? 
A.  54 
B.  16 
C.  10 
D.  35 
Answer» A. 54 
70. 
In q.97. How many know exactly 1 language? 
A.  6 
B.  16 
C.  7 
D.  10 
Answer» C. 7 
71. 
In the class of 55 students the number ofstudying different subjects are as given below: Maths 23, Physics 24, chemistry 19, maths+physics 12, maths+chemistry 9, Physics +chemistry 7, all three subjects 4. Find the number of students who have taken atleast 1 subject? 
A.  22 
B.  45 
C.  42 
D.  14 
Answer» C. 42 
72. 
[~ q ^ (p→q)]→~ p is, 
A.  Satisfiable 
B.  tautology 
C.  unsatisfiable 
D.  contradiction 
Answer» B. tautology 
73. 
If P and Q stands for the statement P : It is hot

A.  It is got and it is humid 
B.  It is hot and it is not humid 
C.  it is not hot and it is humid 
D.  none 
Answer» B. It is hot and it is not humid 
74. 
In a survey of 85 people it is found that 31 like to drink milk, 43 like coffee and 39 like tea.Also 13 like both milk and tea, 15 like milk and coffee, 20 like tea and coffee and 12 like none of the three drinks. Find the number of people who like all the three drinks. 
A.  10 
B.  9 
C.  8 
D.  7 
Answer» C. 8 
75. 
The statement ( p^q) → p is a 
A.  absurdity 
B.  contadiction 
C.  tautology 
D.  none 
Answer» C. tautology 
76. 
Let p be “He is tall” and let q “He is handsome”. Then the statement “It is false that he is short or handsome” is: 
A.  p ^ q 
B.  ~ (~ p ^q) 
C.  p^ ~ q 
D.  ~ p ^q 
Answer» B. ~ (~ p ^q) 
77. 
Let P(S) denotes the powerset of set S. Which of the following is always true? 
A.  P(P(S)) = P(S) 
B.  P(S) IS = P(S) 
C.  P(S) I P(P(S)) = {ø} 
D.  S € P(S) 
Answer» D. S € P(S) 
78. 
Which of the following proposition is a tautology? 
A.  (p v q)→p 
B.  p v (q→p) 
C.  p v (p→q) 
D.  p→(p→q) 
Answer» C. p v (p→q) 
79. 
Which of the following statement is the negation of the statement “4 is even or 5 is negative”? 
A.  4 is odd and 5 is not negative 
B.  4 is even or 5 is not negative 
C.  4 is odd or 5 is not negative 
D.  4 is even and 5 is not negative 
Answer» A. 4 is odd and 5 is not negative 
80. 
Which one is the contrapositive of q → p ? 
A.  p → q 
B.  ~p →~q 
C.  ~q→~p 
D.  None 
Answer» B. ~p →~q 
81. 
Check the validity of the following argument : “If the labour market is perfect then the wages of all persons in a particular employment

A.  Invalid 
B.  Valid 
C.  Both a and b 
D.  None 
Answer» B. Valid 
82. 
∃ is used in predicate calculus

A.  TRUE 
B.  FALSE 
C.  Both a and b 
D.  None 
Answer» A. TRUE 
83. 
∀ is used in predicate calculus

A.  TRUE 
B.  FALSE 
C.  Both a and b 
D.  None 
Answer» A. TRUE 
84. 
“If the sky is cloudy then it will rain and it will not rain” 
A.  absurdity 
B.  contadiction 
C.  tautology 
D.  none 
Answer» C. tautology 
85. 
Represent statement into predicate calculus forms : "Not all birds can fly". Let us assume the following predicates bird(x): “x is bird” fly(x): “x can fly”. 
A.  ∃x bird(x) V fly(x) 
B.  ∃x bird(x) ^ ~ fly(x) 
C.  ∃x bird(x) ^ fly(x) 
D.  None 
Answer» B. ∃x bird(x) ^ ~ fly(x) 
86. 
Represent statement into predicate calculus forms : "If x is a man, then x is a giant." Let us assume the following predicates man(x): “x is Man” giant(x): “x is giant”. 
A.  ∀ (man(x)→ ~giant(x)) 
B.  ∀ man(x)→ giant(x) 
C.  ∀ (man(x)→ giant(x)) 
D.  None 
Answer» C. ∀ (man(x)→ giant(x)) 
87. 
Represent statement into predicate calculus forms : "Some men are not giants." Let us assume the following predicates man(x): “x is Man” giant(x): “x is giant”. 
A.  ∃x man(x) ^ giant(x) 
B.  ∃x man(x) ^ ~ giant(x) 
C.  ∃x man(x) V ~ giant(x) 
D.  None 
Answer» B. ∃x man(x) ^ ~ giant(x) 
88. 
Represent statement into predicate calculus forms : There is a student who likes mathematics but not history. Let us assume the following predicates student(x): “x is student.” likes(x, y): “x likes y”. and ~likes(x, y) “x does not like y”. 
A.  ∃x [student(x) ^ likes(x, mathematics) ^~ likes(x, history)]Q. 
B.  ∃x [student(x) ^Vlikes(x, mathematics) V~ likes(x, history)]Q. 
C.  ∃x [student(x) ^ ~likes(x, mathematics) ^likes(x, history)]Q. 
D.  None 
Answer» A. ∃x [student(x) ^ likes(x, mathematics) ^~ likes(x, history)]Q. 
89. 
AUB = (A− B)U(B−A)U(AпB). 
A.  FALSE 
B.  TRUE 
C.  Both a and b 
D.  None 
Answer» B. TRUE 
90. 
[(PVQ)^(P→R)^(Q→S)] → (SVR). Is a…. 
A.  absurdity 
B.  contadiction 
C.  tautology 
D.  none 
Answer» C. tautology 
91. 
~(x vy) = ~x ^ ~y 
A.  FALSE 
B.  TRUE 
C.  Both a and b 
D.  None 
Answer» B. TRUE 
92. 
(x ^ y)’ = x’ V y’ 
A.  FALSE 
B.  TRUE 
C.  Both a and b 
D.  None 
Answer» B. TRUE 
93. 
Test the validity of argument:“If it rains tomorrow, I will carry my umbrella, if its cloth is mended. It will rain tomorrow and the cloth will not be mended. Therefore I will not carry my umbrella” 
A.  Invalid 
B.  Valid 
C.  Both a and b 
D.  None 
Answer» B. Valid 
94. 
In a group of athletic teams in a certain institute, 21 are in the basket ball team, 26 in the hockey team, 29 in the foot ball team. If 14 play hockey and basketball, 12 play foot ball and basket ball, 15 play hockey and foot ball, 8 play all the three games. (i) How many players are there in all? 
A.  78 
B.  98 
C.  23 
D.  43 
Answer» D. 43 
95. 
In above Q.123 (ii) How many play only foot ball? 
A.  10 
B.  8 
C.  9 
D.  4 
Answer» A. 10 
96. 
(p ↔ q) ↔ r = p ↔ (q ↔ r) 
A.  absurdity 
B.  contadiction 
C.  tautology 
D.  none 
Answer» C. tautology 
97. 
Write the negation in good english sentence : "Jack did not eat fat, but he did eat broccoli." 
A.  If Jack eat and broccoli then he did ate fat. 
B.  If Jack did not eat broccoli then he did ate fat. 
C.  If Jack did not eat broccoli or he did ate fat. 
D.  If Jack did not eat broccoli then he did not ate fat. 
Answer» B. If Jack did not eat broccoli then he did ate fat. 
98. 
Write the negation in good english sentence : The weather is bad and I will not go to work. 
A.  The weather is not bad or I will go to work. 
B.  The weather is good or I will go to work. 
C.  The weather is not bad or I will not go to work. 
D.  None 
Answer» A. The weather is not bad or I will go to work. 
99. 
Write the negation in good english sentence : Mary lost her lamb or the wolf ate the lamb. 
A.  Mary did loss her lamb and the wolf eat the lamb. 
B.  Mary did loss her lamb and the wolf did not eat the lamb. 
C.  Mary did not loss her lamb and the wolf did not eat the lamb. 
D.  None 
Answer» C. Mary did not loss her lamb and the wolf did not eat the lamb. 
100. 
Write the negation in good english sentence : I will not win the game or I will not enter the contest. 
A.  I will not win the game and I will enter the contest. 
B.  I will win the game and I will enter the contest. 
C.  I will win the game and I will not enter the contest. 
D.  None 
Answer» B. I will win the game and I will enter the contest. 
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